The purpose of this model is to understand how genetic architectures of alternative reproductive tactics impact their maintenance in populations. I’m using an individual-based simulation model with different selection scenarios, types of alternative tactics, and genetic architectures (genome-wide additive genetic variance, supergenes, expression networks) To test the model and make sure that everything has been implemented correctly, I’m first testing to ensure that the model produces the expected results without the genetic architectures.

Overview of the model

Males can be courters or not-courters and parents or not-parents. When the model is run with both traits, this results in four possible morphs: courter/parent, courter/not-parent, not-courter/parent, and not-courter/not-parent. In each generation, the population follows the following timeline:

  1. Females choose a nest
  2. Males fertilize eggs
  3. Nests survive or die
  4. Viability selection on progeny
  5. Stochastic survival to adulthood

Choosing a nest

A female samples 50 males and chooses a male to nest with based on his courtship trait. If there are no courtship traits in the model, she chooses based on the male’s parental trait. If she does not encouter an acceptable male, she does not nest. If she encounters multiple equally-acceptable males, she randomly selects one of them.

Fertilization

Once a female decides to nest, up to three males can fertilize the nest. Courters and parental males can contribute more sperm than non-courter and non-parental males – \(r_{courter}=r_{parent}=8\) and \(r_{non-courter}=r_{non-parent}=4\). A courter/non-parent has \(r_{non-parent}\) and a non-courter/parent has \(r_{parent}\). The male with whom the female is nesting gets \(r_{parent}/\Sigma{n_{sperm}}\) and additional sneaker males (up to 2) get \((r_{non-parent}*0.5/\Sigma{n_{sperm}})\), where \(\Sigma{n_{sperm}}\) is the total number of sperm contributed by all of the males, weighted by the sperm competition factor (0.5 is the default for all males except the nesting male). So, when a female mates with one courter and two sneakers, \(\Sigma{n_{sperm}}\) = \(r_{courter}\) + 2\(*\)(0.5\(*\)\(r_{sneaker}\)), where \(r_{courter}\) = 8 and \(r_{sneaker}\) = 4, therefore \(\Sigma{n_{sperm}}\) = 12.

Nest Survival

Before the babies can survive, the nest has to survive. This step is only relevant when parental traits are in the model - if only the courtship trait is specified, then all progeny in the nest survive at this point. When males have the parental trait, if the female has given eggs to a non-parental male (because she chose based on courtship traits), then the nest has a 10% chance of surviving. If the female has given eggs to a parental male, the nest has a 90% chance of surviving.

Viability selection and stochastic survival

Then the offspring experience viability selection. Courters and parental males are disfavored in viability selection, with a survival probability of 0.9950125. If an individual is both a courter and a parental male, the survival probability is 0.9900498. Non-courters and non-parental males have survival probabilities of 1. Once viability selection has been imposed, individuals die or survive randomly, and the next generation gets a chance to mate.

Evaluating equilibrium

After 10000 generations, I evaluate whether the population is at equilibrium. Each generation I track the change in frequency of the courter and parent traits, and I calculate the variance in the change in frequency over those initial 10000 generations. I declare an equilibrium has been reached if the last change in frequency of both traits is less than the variance in changes in frequency. If the last change in frequency is larger than the variance, then I run the model for an additional 2000 generations or until an equilibrium is reached, whichever comes first.

Unlinked additive genetic variance

In these cases, the traits are encoded by a number (50) of loci, whose alleles contribute additively to determine the trait value. These alleles are all freely recombining and are not adhered to any physical genomic location (aka this is a classical quantitative genetics approach). The overall trait value is compared to a population-level threshold (which is static, in these cases), and if the trait value is above the threshold the male takes the parent or courter morph and if it is below he does not. Below, I’m showing the results from 10 replicates of each scenario.

Courter trait

Females choose nests based on whether the male is a courter or not, and they all prefer courters all of the time (the female preference does not have a genetic basis and does not evolve). The only way that non-courters produce offspring is through sneaking, but all males can be sneakers (both courters and non-courters). Because parental care is not incorporated in this model, all nests survive.

Of the 10 replicates, 10 reached an equilibrium by 10000 generations.

The numbers in the bars are the frequencies of each morph in the final generation, and “E” below a set of bars means that replicate resulted in an equilibrium and “N” means it did not reach an equilibrium.

Frequency of courters in final generation
CourterFreq CourterW NonCourterW
Rep1 1 3.06299 0
Rep2 1 3.01961 0
Rep3 1 3.26994 0
Rep4 1 3.09145 0
Rep5 1 3.50107 0
Rep6 1 3.32017 0
Rep7 1 3.11245 0
Rep8 1 3.19433 0
Rep9 1 3.45781 0
Rep10 1 2.98047 0

Parental trait

All females nest with parental males, so the only way non-parental males reproduce is through sneaking. Parental males provide care that allows nests to have a 90% chance of survival. The female preference does not have a genetic basis and does not evolve.

Of the 10 replicates, 10 reached an equilibrium by 10000 generations.

The numbers in the bars are the frequencies of each morph in the final generation, and “E” below a set of bars means that replicate resulted in an equilibrium and “N” means it did not reach an equilibrium.

Frequency of parents in final generation
ParentFreq ParentW NonParentW
Rep1 1 3.54071 0
Rep2 1 3.57113 0
Rep3 1 3.55940 0
Rep4 1 3.46260 0
Rep5 1 3.45059 0
Rep6 1 3.49801 0
Rep7 1 3.47036 0
Rep8 1 3.37282 0
Rep9 1 3.33654 0
Rep10 1 3.61345 0

Courtship and Parental Traits

Females choose nests based on males’ courtship trait (they all only nest with courting males, and the female preference does not have a genetic basis and does not evolve), and then the survival of the nest depends on whether the courting male is also a parental male. If the chosen male is a parental male, the nest has a 90% chance of survival. Otherwise, it only has a 10% chance. Non-courters only reproduce through sneaking.

Frequency of the two morphs (courter = green, parent = blue)

Frequency of the two morphs (courter = green, parent = blue)

The different runs have different outcomes.

Let’s look at the morph frequencies.

The second panel in the top row shows a run where the population crashed after 12 generations.

We can look at the final frequencies in a table as well:

Frequency of morphs in final generation
FreqNcNp FreqCNp FreqNcP FreqCP
Rep1 0 0.000000 0.000000 1
Rep2 0 0.333333 0.666667 0
Rep3 0 0.000000 0.000000 1
Rep4 0 0.603604 0.396396 0
Rep5 0 0.000000 0.000000 1
Rep6 0 0.000000 0.000000 1
Rep7 0 1.000000 0.000000 0
Rep8 0 0.000000 0.000000 1
Rep9 0 0.962963 0.037037 0
Rep10 0 0.000000 0.000000 1

Multiple morphs are maintained in 3 of the 10 replicates, and those morphs contain either a parent or a courter.

Courtship + Negative Frequency Dependent Selection

In this case, the female preference is based on the frequency of the courtship morphs in the population - females prefer the less frequent morph. Everything else is the same as above; all nests survive since parental care is not incorporated in this model, and courters and parental males are disfavored in viability selection.

Courter Frequncies with negative frequency dependent preferences
Generation CourterFreq CourterW NonCourterW
Rep1 9999 0.584178 2.99653 3.34146
Rep2 9999 0.571121 3.63396 3.50754
Rep3 9999 0.616803 3.08306 3.39037
Rep4 11999 0.534137 3.09023 3.19828
Rep5 9999 0.634343 2.89490 3.22652
Rep6 9999 0.552209 2.98182 3.19283
Rep7 11999 0.552361 3.14126 3.27064
Rep8 9999 0.500924 2.28782 2.82222
Rep9 9999 0.558000 2.91039 3.19910
Rep10 11999 0.520170 3.60816 3.38496

With negative frequency dependent preferences, both courters and non-courters are maintained in the population.

Parenting + Negative Frequency Dependent Selection

In this case, the female preference is based on the frequency of the parental morphs in the population - females prefer the less frequent morph. Everything else is the same as above; nests given to parents have a 90% chance of survival and a 10% chance of survival if given to non-parents, and courters and parental males are disfavored in viability selection.

Parent Frequncies with negative frequency dependent preferences
Generation ParentFreq ParentW NonParentW
Rep1 6 0.750000 0 0
Rep2 3 0.846154 0 0
Rep3 5 0.714286 0 0
Rep4 6 0.500000 0 0
Rep5 9 0.833333 0 0
Rep6 6 1.000000 0 0
Rep7 23 0.000000 0 0
Rep8 23 0.500000 0 0
Rep9 46 0.518519 0 0
Rep10 1 0.000000 0 0

When negative frequency dependent preferences are acting on the parental traits, the population crashes.

Courtship + Parenting + Negative Frequency Dependent Selection

In this case, the female preference is based on the frequency of the courtship morphs in the population - females prefer the less frequent morph. Everything else is the same as above; parental males’ nests survive with a probability of 90% and non-parental males’ nests survive with a probability of 10%, and courters and parental males are disfavored in viability selection.

Morph Frequencies with negative frequency dependent preferences
FreqNcNp FreqCNp FreqNcP FreqCP
Rep1 0.0000000 0.333333 0.666667 0.000000
Rep2 0.0000000 0.000000 1.000000 0.000000
Rep3 0.0759494 0.000000 0.000000 0.924051
Rep4 0.0000000 0.214286 0.785714 0.000000
Rep5 0.1818180 0.000000 0.000000 0.818182
Rep6 0.1666670 0.000000 0.000000 0.833333
Rep7 0.3846150 0.000000 0.000000 0.615385
Rep8 0.3333330 0.000000 0.000000 0.666667
Rep9 0.0000000 0.400000 0.600000 0.000000
Rep10 0.1666670 0.000000 0.000000 0.833333

When negative frequency dependent preferences are acting on the courtship traits and there are parent traits as well, the population crashes.

Courtship + Heritable Female Preferences

Here, the female preference has unlinked additive genetic variance that is inherited. The traits begin as uncorrelated and are not pleiotropic (i.e., they have different genes underlying them). A threshold is set in the first generation that determines the switch point for when females prefer courters or non-courters. This threshold does not change over the generations. All males can be sneakers, but the male who females choose to nest with get a first male advantage.

Courter Frequncies with heritable female preferences
Generation CourterFreq CourterW NonCourterW
Rep1 9999 0.713675 3.48503 3.34328
Rep2 9999 0.459350 3.25221 3.16165
Rep3 9999 0.724206 2.93699 3.07194
Rep4 9999 0.494141 2.82609 2.91892
Rep5 9999 1.000000 2.91506 0.00000
Rep6 9999 1.000000 2.99419 0.00000
Rep7 9999 1.000000 3.25358 0.00000
Rep8 9999 0.850288 2.87810 2.17949
Rep9 9999 1.000000 3.25410 0.00000
Rep10 11999 0.430279 3.01852 3.04545

Evolving female preferences allow variation to be maintained.

Parenting + Heritable Female Preferences

Here, the female preference has unlinked additive genetic variance that is inherited. The traits begin as uncorrelated and are not pleiotropic (i.e., they have different genes underlying them). A threshold is set in the first generation that determines the switch point for when females prefer parents or non-parents. This threshold does not change over the generations. Only non-parental males can be sneakers, and when females choose to mate with non-parents, the nest has a 10% survival rate.

Parent Frequncies with heritable female preferences
Generation ParentFreq ParentW NonParentW
Rep1 2578 0.4000000 0.00000 0.000000
Rep2 9999 1.0000000 3.67164 0.000000
Rep3 9999 0.2121210 1.14286 0.173077
Rep4 9999 0.3965520 0.00000 0.400000
Rep5 157 0.3529410 0.00000 0.000000
Rep6 11999 0.0185185 0.00000 0.264151
Rep7 533 0.8750000 0.00000 0.000000
Rep8 9999 1.0000000 3.34216 0.000000
Rep9 11999 0.7433860 2.56584 0.731959
Rep10 9999 1.0000000 3.19132 0.000000

Evolving female preferences maintain variation, although parental traits can lead to population crashes (in 3 of the 10 reps).

Courthip and Parenting + Heritable Female Preferences

Here, the female preference has unlinked additive genetic variance that is inherited. The traits begin as uncorrelated and are not pleiotropic (i.e., they have different genes underlying them). A threshold is set in the first generation that determines the switch point for when females prefer courters or non-courters. This threshold does not change over the generations. Only non-parental males are sneakers, and when females choose to mate with non-parents, the nest has a 10% survival rate.

Morph Frequencies with heritable preferences
FreqNcNp FreqCNp FreqNcP FreqCP
Rep1 0.00 0.000000 0.0000000 1.00
Rep2 1.00 0.000000 0.0000000 0.00
Rep3 0.00 0.000000 0.0000000 1.00
Rep4 0.00 0.966102 0.0338983 0.00
Rep5 0.00 0.866667 0.1333330 0.00
Rep6 0.00 0.000000 1.0000000 0.00
Rep7 0.00 0.000000 0.0000000 1.00
Rep8 0.00 0.000000 1.0000000 0.00
Rep9 0.00 0.294821 0.7051790 0.00
Rep10 0.25 0.000000 0.0000000 0.75

Again, evolving preferences maintain variation. 2 of the 10 populations crashed, though.